I think all the 040 accelerators for the A1200 take 72-pin SIMMs, which are easy enough to find second-hand. Which 1240 specifically do you have? e.g., a Blizzard or something else? Some accelerators require certain physical characteristics for their memory--for example, I recall that Blizzard 1240/1260 boards need single-sided SIMMs; if there are chips on both sides it won't fit in the slot.
That should be a pretty zippy system once you get some RAM onboard!